Lifting wreath product extensions

Black, Elena

doi:10.1090/S0002-9939-00-05797-X

Lifting wreath product extensions
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by Elena V. Black PDF

Proc. Amer. Math. Soc. 129 (2001), 1283-1288 Request permission

Abstract:

Let $G$ and $H$ be finite groups and let $K$ be a hilbertian field. We show that if $G$ has a generic extension over $K$ and $H$ satisfies the arithmetic lifting property over $K$, then the wreath product $G\wr H$ of $G$ and $H$ also satisfies the arithmetic lifting property over $K$. Moreover, if the orders of $H$ and $G$ are relatively prime and $G$ is abelian, then any extension of $G$ by $H$ (which is necessarily a semidirect product) has the arithmetic lifting property.

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